Question 2 (Total: 20 marks) (a) Consider a whole life disability income insurance policy issued to a healthy life aged x. Let State 0 denotes Healthy, State 1 denotes Sick and State 2 denotes Death. Mortality follows the Standard Sickness-Death Model and the effective interest rate is 5% per annum. An annual premium, P, is payable continuously while the person is in the healthy state. A benefit of $1,000 per year is payable continuously while the person is in the sick state. A death benefit of $20,000 is payable immediately upon death. 02 Write down the integral formula for " and Ax . (2 marks) ij (ii) Write down a formula in terms of " and A functions of the benefit reserve at time t for this policy, assuming the life is at healthy state. (2 marks) (iii) For a healthy life aged 50, find the value of P for this policy. (4 marks) Question 2 (Total: 20 marks) (a) Consider a whole life disability income insurance policy issued to a healthy life aged x. Let State 0 denotes Healthy, State 1 denotes Sick and State 2 denotes Death. Mortality follows the Standard Sickness-Death Model and the effective interest rate is 5% per annum. An annual premium, P, is payable continuously while the person is in the healthy state. A benefit of $1,000 per year is payable continuously while the person is in the sick state. A death benefit of $20,000 is payable immediately upon death. 02 Write down the integral formula for " and Ax . (2 marks) ij (ii) Write down a formula in terms of " and A functions of the benefit reserve at time t for this policy, assuming the life is at healthy state. (2 marks) (iii) For a healthy life aged 50, find the value of P for this policy. (4 marks)